CONVOLUTIONS OF THE VON MANGOLDT FUNCTION OVER RESIDUE CLASSES

Author:

Frederike~R\"UPPEL

2010 Mathematics Subject Classification:

11M32.

Keywords:

Dirichlet L-function, double Dirichlet series, multiple Dirichlet series, Riemann zeta-function, residue classes.

Abstract:

We consider a Dirichlet series associated to the number of representations of an integer as a sum of primes from certain residue classes. Using techniques due to Matsumoto and Egami [4], we prove similar results about the analytic behaviour of this series. This is related to the Goldbach conjecture with residue class conditions.

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Rupp-2012

Vol. 7 (15), 2011